Library 

Citrus  Expei  i«"litl  Cation 
University  ot  California 
S.  DEPARTMENT  OF  AGRICULTURE, 

BUREAU  OF  ANIMAL  INDUSTRY.— BULLETIN  124. 
A.  D.  MELVIN,  CHIEF  OF  BUREAU. 


METHODS  AND  STANDARDS  IN 
BOMB  CALORIMETRY. 


INVESTIGATIONS  IX  COOPERATION  WITH  THE  INSTITUTE  OF 
ANIMAL  NrTKITION  OF  THE  PENNSYLVANIA  STATE  COLLEGE. 


i\lk  Pkl   IDS 


BY 


\ 


CD 


t-b 


-2/L 


].  AUGUST   FRIF.S, 


Assistant  /:".r/V;7  in  Annual  Xutrition 


WASHINGTON: 

GOVERNMENT   PRINTING   OFFICE. 
1910. 


library 

Citrus  Experiment  Station 

I  I  ri  i  i/ 1, ,-.  IT          Jailed  August  29,  1910. 

Umveisity  of  taliforrija 
U.  S.  DEPARTMENT  OF  AGRICULTURE, 

BUREAU  OF  ANIMAL  INDUSTRY.— BULLETIN  124. 

A.  D.  MELVIN,  CHIEF  OF  BUREAU. 


METHODS  AND  STANDARDS  IN 
BOMB  CALORIMETRY. 


INVESTIGATIONS  IN  COOPERATION  WITH  THE  INSTITUTE  OF 
ANIMAL  NUTRITION  OF  THE  PENNSYLVANIA  STATE  COLLEGE. 


BY 

J.  AUGUST  FRIES, 
Assistant  Expert  in  Animal  Nutrition. 


WASHINGTON: 

GOVERNMENT    PRINTING    OFFICE. 

1910. 


THE  BUREAU  OF  ANIMAL  INDUSTRY. 


Chief:  A.  D.  MELVIN. 
Assistant  Chief:  A.  M.  FAKRINGTON. 
Chief  Cleric:  CHARLES  C.  CARROLL. 

Animal  Husbandry  Division:  GEORGE  M.  ROMMEL,  chief. 
Biochemic  Division:  M.  DORSET,  chief. 
Dairy  Division:  B.  H.  RAWL,  chiet. 

Inspection  Division:  RICE  P.  STEDDOM,  chief;  MORRIS  WOODEN,  R.  A.  RAMSAY, 
and  ALBERT  E.  BEHNKE,  associate  chiefs. 
Pathological  Division:  JOHN  R.  MOHLER,  chief. 
Quarantine  Division:  RICHARD  W.  HICKMAN,  chief. 
Zoological  Division:  B.  H.  RANSOM,  chief. 
Experiment  Station:  E.  C.  SCHROEDER,  superintendent. 
Editor:  JAMES  M.  PICKENS. 
2 


LETTER  OF  TRANSMITTAL. 


U.  S.  DEPARTMENT  OF  AGRICULTURE, 

BUREAU  OF  ANIMAL  INDUSTRY, 

Washington,  D.  C.,  May  5,  1910. 

SIR;  I  have  the  honor  to  transmit  and  to  recommend  for  pub- 
lication in  the  bulletin  series  of  this  Bureau  a  manuscript  entitled 
"Methods  and  Standards  in  Bomb  Calorimetry,"  by  J.  August  Fries, 
assistant  expert  in  animal  nutrition. 

The  investigation  described  is  a  continuation  of  that  already 
reported  in  Bulletin  94  of  this  Bureau,  and  is  connected  with  the 
work  in  animal  nutrition  conducted  at  State  College,  Pa.,  by  coopera- 
tion between  the  institute  of  animal  nutrition  of  the  Pennsylvania 
State  College  and  this  Bureau  through  its  Animal  Husbandry  Divi- 
sion. The  particular  objects  sought  to  be  attained  by  Mr.  Fries  in  the 
present  paper  are  set  forth  in  the  accompanying  letter  of  Doctor 
Armsby,  the  expert  in  direct  charge  of  the  cooperative  investigations. 
Respectfully, 

A.  D.  MELVIN, 

Chief  of  Bureau. 
Hon.  JAMES  WILSON, 

Secretary  of  Agriculture. 


LETTER  OF  SUBMITTAL. 


STATE  COLLEGE,  PA.,  October  20,  1909. 

SIR: 'I  have  the  honor  to  submit  herewith  the  results  of  experi- 
ments by  Mr.  J.  August  Fries,  M.  S.,  assistant  expert  in  animal  nutri- 
tion, upon  "Methods  and  Standards  in  Bomb  Calorimetry." 

The  accurate  determination  of  the  heats  of  combustion  of  organic 
substances  is  not  only  a  fundamental  requirement  in  the  nutrition 
investigations  now  being  conducted  in  cooperation  with  the  insti- 
tute of  animal  nutrition  of  the  Pennsylvania  State  College,  but  is  of 
great  importance  in  many  other  lines  of  both  scientific  and  technolog- 
ical research.  Mr.  Fries's  investigations  are  a  continuation  of  those 
reported  in  Bulletin  94  of  the  Bureau  of  Animal  Industry  and  deal 
essentially  with  the  standardization  of  methods  as  a  means  of  secur- 
ing results  which  shall  be  comparable  among  themselves  and  bear  a 
definite  relation  to  established  physical  constants.  To  this  end  a  new 
method  of  determining  the  hydrothermal  equivalent  of  the  bomb 
calorimeter  has  been  devised;  the  influence  of  impurities  in  the  oxy- 
gen used,  as  well  as  of  some  other  minor  sources  of  error,  has  been 
studied;  and  a  redetermination  of  the  heat  of  combustion  of  benzoic 
acid  has  been  made  with  reference  to  its  acceptance  as  a  standard 
substance  in  bomb  calorimetry. 

It  is  believed  that  the  results  of  these  investigations  will  be  of 
interest  and  value  to  all  experimenters  who  use  the  bomb  calorimeter 
for  any  purpose. 

Very  respectfully,  HENRY  PRENTISS  ARMSBY, 

Expert  in  Animal  Nutrition. 

Dr.  A.  D.  MELVIN, 

Chief  of  the  Bureau  of  Animal  Industry. 
4 


CONTENTS* 


Page. 

Introduction 7 

Hydrothermal  equivalent  of  the  calorimeter 7 

Necessity  of  a  common  standard 8 

Determination  of  the  water  value  of  the  bomb  calorimeter 8 

By  computation  of  component  parts 9 

The  electric  method 10 

Error  due  to  evaporation  of  water 14 

A  third  method 19 

Displacement  of  water 19 

Water  value  of  the  calorimeter 21 

Correction  for  combustible  gases  in  the  oxygen 22 

Nature  of  combustible  gases 26 

The  heat  of  combustion  of  benzoic  acid 26 

Sulphur,  phosphorus,  and  chlorin 28 

Correction  for  specific  heat  of  water 28 

Change  in  the  bomb  contents 28 

Change  of  pressure  in  the  bomb 30 

Use  of  the  bomb  calorimeter  under  different  conditions 31 

Corrections  for  impurities  in  oxygen 32 

Benzoic  acid  as  a  standard 32 

5 


Citrus  LxKi,i,,e,,t  Station 
University  of  California 


METHODS  AND  STANDARDS  IN  BOMB  CALORIMETRY. 


INTRODUCTION. 

The  bomb  calorimeter  not  only  is  coming  more  and  more  into  use 
in  research  and  instruction  laboratories,  but  has  also  found  large 
practical  application  in  fuel-testing  laboratories,  and  is  beginning  to 
find  a  place  of  usefulness  as  a  method  of  chemical  analysis.  With 
this  increase  in  bomb-calorimeter  work,  and  consequently  increased 
publication  of  results,  one  fact  has  been  brought  out  very  clearly, 
namely,  that  there  is  at  present  great  lack  of  uniformity  in  the  work. 
Reports  of  the  work  done  in  these  various  kinds  of  laboratories,  by 
differently  trained  men  using  different  types  of  bomb  calorimeters, 
seem  to  indicate  that  calorimetry,  instead  of  becoming  more  per- 
fected and  reliable  by  wider  application,  is  in  a  sense  becoming  more 
chaotic.  One  man's  work  can  not  readily  be  compared  with  that  of 
another.  A  calorie,  in  other  words,  is  not  a  definite  fixed  quantity, 
as  it  should  be  in  bomb-calorimeter  work,  since  no  two  persons  neces- 
sarily agree  concerning  what  standard  to  use. 

HYDROTHERMAL    EQUIVALENT    OF   THE    CALORIMETER. 

Each  individual  bomb  calorimeter  must  have  its  hydrothermal 
equivalent,  or  water  value,  determined;  that  is,  the  number  of  calo- 
ries required  to  raise  the  mass  of  water  and  metal  one  degree  Centi- 
grade. Preferably,  this  should  be  done  at  the  place  where  it  is  to  be 
used,  and  by  the  individual  who  is  to  be  responsible  for  the  work. 
For  this  purpose  it  is  customary  to  burn  substances — like  benzoic 
acid,  naphthalin,  camphor,  cellulose,  sugar,  etc. — of  known  chemical 
composition,  which  as  a  rule  burn  readily,  can  easily  be  obtained  in  a 
high  state  of  purity,  and  whose  heats  of  combustion  are  supposed  to 
be  known.  As  to  the  choice  of  a  substance  against  which  to  stand- 
ardize the  apparatus,  however,  the  investigators  or  operators  do  not 
agree,  each  selecting  according  to  his  own  fancy  and  convenience,  or 
as  influenced  by  some  one  else.  Thus,  some  may  use  several  sub- 
stances while  others  choose  only  one.  One  set  of  analysts  use  naph- 
thalin and  give  it  a  heat  value  of  9,628  calories  per  gram,  while  others 
using  the  same  substance  give  it  a  heat  value  of  9,696  calories  per 
gram.  Some  use  benzoic  acid,  accepting  6,322  calories  per  gram  as 
its  heat  of  combustion  value,  while  others  regard  this  as  too  low,  and 

7 


8  METHODS  AND  STANDAKDS  IN  BOMB  CALOEIMETRY. 

use  6,335  or  some  other  number  of  calories  as  the  correct  value  for  the 
standard  on  which  their  work  is  based.  Such  cases  could  be  multi- 
plied. Each  man  for  himself,  apparently,  is  the  condition. 

NECESSITY    OF    A    COMMON    STANDARD. 

Now,  if  work  of  this  nature  is  to  reach  its  greatest  usefulness — that 
is,  if  the  work  of  each  individual  is  to  be  relied  upon  to  mean  a  defi- 
nite thing  and  thus  be  of  use  to  everybody  else  interested  in  the  same 
line  of  work — then  we  need  above  all  things  one  common  standard. 
The  writer  believes  that  it  is  high  time  that  some  single  substance  be 
chosen,  a  heat  value  agreed  upon,  and  that  substance  in  some  way 
recognized  as  a  standard  for  bomb-calorimeter  work.  In  the  future, 
should  the  heat  value  of  such  a  substance  have  to  be  slightly  changed, 
results  would  still  be  useful  and  comparable  after  a  little  calculation. 

From  his  own  personal  experience  with  the  substances  mentioned, 
the  writer  believes  that  benzoic  acid  meets  the  requirements  for  a 
standard  better  than  any  of  the  other  substances,  and  considers  it 
the  most  suitable  that  could  be  selected  for  such  a  standard.  It  was, 
therefore,  for  the  purpose  of  calling  attention  to  existing  conditions 
and  with  the  hope  of  perchance  being  able  to  do  something  which 
should  help  to  bring  to  pass  in  the  near  future  the  adoption  of  such  a 
standard  that  a  redetermination  of  the  heat  of  combustion  of  benzoic 
acid  was  undertaken. 

The  plan  of  the  undertaking  was  to  determine  again  the  heat  of 
combustion  of  benzoic  acid,  independently  of  all  previous  determina- 
tions of  the  heat  of  combustion  of  any  organic  substance  whatsoever, 
using  an  improved  bomb,  calorimeter  recently  described.0  The 
problem  itself,  which  it  was  desired  to  work  out  step  by  step,  with 
reference  to  the  material  and  apparatus  on  hand,  can  be  stated  as 
follows : 

Having  a  new  bomb  calorimeter  of  unknown  hydrothermal  equiva- 
lent, or  water  value,  also  an  oxygen  supply  of  undetermined  correc- 
tion for  any  combustible  gases  which  may  be  present  as  impurity, 
and  assuming  that  no  organic  substance  exists  which  has  had  its  heat 
of  combustion  accurately  determined  so  as  to  be  referred  to  or 
accepted  as  a  standard;  to  determine  the  heat  of  combustion  of 
benzoic  acid. 

DETERMINATION  OF  THE  WATER  VALUE  OF  THE  BOMB  CALO- 
RIMETER. 

The  first  requirement  in  order  to  solve  the  problem  before  us  is  to 
determine  the  water  equivalent  of  the  whole  bomb-calorimeter  sys- 
tem, assuming  also  that  no  substance  with  a  known  heat  of  combus- 
tion value  was  to  be  had.  In  order  to  determine  this  water  value  of 

a  The  Journal  of  the  American  Chemical  Society,  Vol.  XXI,  p.  272,  1908. 


DETERMINATION  OF  WATER  VALUE.  9 

the  apparatus  two  known  methods,  one  of  which  at  least  is  frequently 
referred  to  in  connection  with  the  bomb  calorimeter,  were  used,  and 
also  a  third  method  devised  by  the  writer. 

BY  COMPUTATION  OF  COMPONENT  PARTS. 

The  first  and  more  commonly  used  of  the  two  known  methods  con- 
sists in  computing  from  the  weight  of  each  of  the  component  parts  of 
the  bomb  system  and  the  corresponding  specific  heats  the  water  value 
of  each  substance,  the  sum  of  all  giving  the  water  equivalent  of  the 
whole  system  or  apparatus.  This  method  is  not  necessarily  abso- 
lutely correct,  since  the  weight  of  some  of  the  parts  can  only  be 
known  approximately,  as,  for  instance,  the  glass  and  mercury  of  the 
thermometer,  small  rubber  pieces,  etc.,  which  can  not  be  discon- 
nected or  weighed.  Further,  the  specific  heat  of  the  particular  steel 
used  for  the  bomb  itself  has  not  been  determined,  nor  is  it  certain 
that  the  other  specific  heats  are  all  absolutely  correct.  However, 
while  we  can  not  claim  absolute  correctness  for  this  method,  the  total 
value  obtained  for  the  whole  system,  including  the  water,  need  not 
vary  more  than  a  few  hundredths,  or  at  most  a  very  few  tenths,  of  1 
per  cent  from  the  true  water  value. 

The  apparatus  in  question  was  an  Atwater-Hempel  bomb  calori- 
meter, having  the  top  modified  so  as  to  permit  the  determination 
of  the  carbon  dioxid  after  a  combustion.  The  modification  consists 
in  having,  besides  the  usual  valve  and  opening  for  the  intake  of 
oxygen,  an  outlet  terminating  in  a  platinum  tube  near  the  bottom  of 
the  bomb  and  through  which  the  gases  are  removed  for  analysis. 

From  the  weight  of  each  of  its  different  parts  and  their  respective 
specific  heats,  the  following  water  value  for  the  bomb  calorimeter 
system  was  obtained: 

TABLE  1. — Computed  water  value  of  bomb  calorimeter. 


Material.                                                     Weight. 

Specific          Water 
heats.        equivalent. 

Grams. 
Steel  3,230.0 

Grams. 
oQ.1114              300  49 

Platinum  1%.  0 

a.  0320                     .  27 

Lead  ......                                                                                  66.  0 

a  0300                       98 

German  silver  (approximate)  .                                              4.0 

a.0940  ;                  .38 

Rubber  (approximate)  4.0 

6.  3310                    .  32 

Iron  (approximate)                                                                                        10.0 

a.1114                      11 

Mercury  (approximate)  50.0 

o.0330                    .65 

Glass  (approximate)  10.  0 

0.1900                    .90 

Britannia  metal.     .                                                                                     855.0 

a.  0548                 46.85 

Oxygen  (constant  volume)  11.4 

a.  1570                   1.79 

Water  at  22°  C  2,000.0 

f.9975           1,995.00 

Total  

2,418.74 

a  The  Journal  of  the  American  Chemical  Society.    Vol.  XXV,  p.  (194.    1903. 

bll.  W.  Wiley.    Principles  and  Practice  of  Agricultural  Analysis.    Vol.  Ill,  p.  573. 

<•  Annalen  der  Physik.  ser.  4,  16,  010  (1905.) 

44865°— Bull.  124—10 2 


10  METHODS  AND   STANDARDS  IN   BOMB  CALOKIMETRY. 

Except  in  the  cases  of  rubber  and  water,  the  specific  heats  used  in 
the  above  computation  are  those  used  by  Atwater  in  determining 
the  water  value  of  his  bomb  calorimeter.  For  the  small  quantity  of 
iron  in  the  connectors  the  same  specific  heat  is  used  as  for  the  steel. 
The  specific  heat  of  water  is  the  average  result  of  Dieterici  and 
Barnes's  determinations. 

According  to  Table  1,  the  total  water  equivalent  of  the  whole 
bomb-calorimeter  system,  including  the  water,  is  2,418.74,  or  without 
the  water  it  is  423.74.  Should  the  other  value  given  by  Atwater  for 
steel  (0.1087  specific  heat)  be  used,  the  water  equivalent  would  be 
415,  or  2,410  including  the  water.  The  water  in  which  the  bomb 
is  immersed  and  through  which  the  heat  is  measured  should  always 
be  the  same  in  amount  in  order  to  insure  the  same  water  level 
in  the  cylinder,  thus  keeping  the  conditions  unchanged.  With  this 
apparatus  2,000  grams  of  water  will  immerse  the  bomb  completely, 
and  is  the  quantity  which  was  uniformly  employed. 

THE    ELECTRIC    METHOD. 

The  second  method  employed  in  determining  the  water  equivalent 
consisted  in  generating  a  measured  amount  of  heat  in  the  bomb  by 
means  of  an  electric  current  passing  through  a  resistance  coil.  The 
generation  of  heat  in  the  bomb  and  the  measurement  of  the  rise  in 
temperature  due  to  it  were  done  under  the  same  conditions  as  when 
a  substance  is  burned  for  its  energy  determination,  except  that  no 
oxygen  was  introduced  into  the  bomb.  Correction,  therefore,  must 
be  made  for  the  usual  amount  of  oxygen  in  computing  the  results. 

The  test  was  made  in  the  following  manner:  About  10  inches  of 
size  26  B.  &  S.  =  0.016  "nichrome"  resistance  wire  was  made  into  a 
small  coil  which  was  connected  to  the  two  platinum  wires  in  the 
bomb  in  such  a  manner  that  the  heat  would  be  generated  at  about 
the  same  place  as  where  the  substances  analyzed  are  burned.  The 
resistance  of  this  wire  coil  was  about  1.38  ohms.  Next,  the  bomb 
was  closed,  placed  in  the  water,  and  connected  up  as  for  a  determina- 
tion of  heat  of  combustion,  and  the  two  insulated  copper  wires  lead- 
ing from  the  bomb  were  connected  to  the  electrical  instrument.  The 
electric  current  was  supplied  by  six  storage  cells  and  was  measured 
by  voltmeter  and  ammeter.  After  starting  the  stirrer  and  taking 
the  usual  few  minutes  preliminary  readings  of  the  water  tempera- 
tures, the  switch  was  closed  at  a  given  signal  and  the  current  from 
the  six  cells  sent  through  the  bomb.  It  was  allowed  to  flow  through 
for  a  number  of  minutes,  the  readings  of  the  voltmeter  and  ammeter 
being  taken  every  half  minute.  The  water  temperature  was  taken 
every  minute  by  means  of  a  Beckman  thermometer  read  to  0.001°  C. 
During  the  first  few  trials  the  voltmeter  and  ammeter  used  were  the 


ELECTRIC   METHOD   OF   DETERMINING   WATER  VALUE. 


11 


commercial,  so-called  American,  instruments,  the  ammeter  having  an 
external  shunt. 

The  various  observations  noted  during  one  of  these  trials  in  which 
the  electric  current  was  on  continuously  for  12  minutes  are  found 
in  Table  2. 

TABLE  2. — Electric  determination  of  voter  equivalent. 


Period. 

Time. 

Temperature  of  calo- 
rimeter. 

Voltmeter. 

Ammeter. 

As  read. 

Corrected. 

Preliminary.  ... 

Minutes. 
1.0 
2.0 
3.0 
4.0 
5.0 

°  C. 
1.236 
1.239 
1.244 
1.247 
1.252 

0  C. 
1.2432 

Volts. 

A  mperes. 

Current  on  

1.2592 

5.5 

11.68 
11.62 
11.60 
11.60 
11.59 
11.59 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 
11.58 

4.62 
4.60 
4.60 
4.60 
4.58 
4.58 
4.58 
4.58 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 
4.60 

Equalizing  

6.0 
6.5 
7.0 
7.5 
8.0 
8.5 
9.0 
9.5 
10.0 
10.5 
11.0 
11.5 
12.0 
12.5 
13.0 
13.5 
14.0 
14.5 
15.0 
15.5 
16.0 
16.5 
17.0 

1.370 

1.3781 

1.660 

1.6696 

1.970 

1.9807 

2.280 

2.2918 

2.595 

2.6084 

2.910 

2.9240 

3.225 

3.2385 

3.545 

3.5567 

3.845 

3.8564 

4.155 

4.1667 

4.470 

4.4816 

4.780 

4.7914 

18.0              4.974 
19.0              5.005 
20.  0              5.  008 
21.0  i            5.009 

4.98(10 
5.0170 
5.0200 
5.0210 

End  period  

22.0              5.006 
23.0              5.004 
24.  0              5.  001 
25.  0              4.  998 

5.0100 

The  ammeter  used  had  an  initial  correction  of  0.16,  which  has  to 
be  added  to  the  average  of  the  readings.  Accordingly,  the  average 
for  the  current  was: 

For  total  time,  11.588  volts,  4.757  amperes;  for  last  8  minutes,  11.58  volts. 

4.76  amperes. 
Room  temperature,  24°  C. 
Temperature  of  water  at  beginning,  21.2°  C. 
Temperature  of  water  at  end,  25.0°  0 

Most  of  the  figures  found  in  the  second  column  of  Table  '2  wore 
read  when  the  mercury  column  in  the  thermometer  was  moving 
rather  fast,  hence  a  ±  error  of  ono  or  two  thousandths  of  a  degree 
could  readily  be  made,  but  any  error  of  that  kind  is  reduced  to  a 


12  METHODS  AND   STANDAEDS   IN   BOMB   CALORIMETRY. 

minimum  by  the  number  of  readings  taken.  If  we  examine  the 
table,  we  notice  that  from  about  the  third  minute  there  was  a  uniform 
increase  in  temperature  of  the  bomb  system,  while  the  voltmeter 
and  ammeter  remained  unchanged,  indicating  a  constant  current. 
Because  of  this  constancy,  as  regards  both  the  current  and  the  rise 
in  temperature  of  the  calorimeter,  the  results  of  the  test  can  be 
worked  out  either  from  the  total  rise  in  temperature  and  total  heat 
generated,  or  from  a  section  of  the  time  consisting  of  the  last  8  or  9 
minutes. 

The  radiation  correction,  or  correction  due  to  the  influence  of  the 
surrounding  air  conditions,  in  the  case  of  the  electric  tests,  as  well  as 
in  all  the  following  determinations  of  heats  of  combustion,  has  been 
worked  out  by  using  the  Regnault-Pfaundler  formula  a— 

v-v'/n-l  ,  dn  +  6, 


y  0  =  sum  of  readings  minus  1  increased  by  an  arbitrary  factor  2  „    * 

v=  average  rate  of  radiation  during  preliminary  period. 
v'  =  average  rate  of  radiation  during  end  period. 
6n  =  number  of  readings  during  combustion  period. 
t  =  average  of  preliminary  thermometer  readings. 
t'  =  average  of  end  period  thermometer  readings. 
Applying  the  correction  thus  found  to  the  entire  test  represented 
by  Table  2,  we  have: 

Last  reading  of  the  heating  period  ...........................  +5.  0210 

First  reading  of  the  heating  period  ...........................  —1.  2592 

Radiation  correction  ........................................  —  .  0029 

Correction  for  thermometer  lag  ...............................  —  .  0010 

Total  rise  in  temperature  ..............................       3.  7579 

If  we  take  a  section  consisting  of  the  last  8  minutes  of  the  test, 
and  represent  by  means  of  a  curve  the  gain  and  loss  to  the  system 
by  radiation,  we  obtain  a  correction  of  +0.0013°  C.  and  a  correction 
for  thermometer  lag  of  —0.0005°  C.  Applying  these  corrections  to 

the  last  8  minutes,  we  have: 

°c 
Thermometer  reading  for  the  twelfth  minute  ................   +4.  7914 

Thermometer  reading  for  the  fourth  minute  .................    —2.  2918 

Radiation  correction  ........................................   +  .  0013 

Correction  for  thermometer  lag  .............................    —  .  0005 

Corrected  rise  for  8  minutes  ............................       2.  5004 

In  computing  the  heat  generated  in  the  bomb  by  the  electric  cur- 
rent and  the  corresponding  water  equivalent  of  the  apparatus  the 

a  H.  W.  Wiley.     Principles  and   Practice  of  Agricultural  Analysis.      1897.     Vol. 
Ill,  p.  572. 


ELECTRIC  METHOD  OF  DETERMINING  WATER  VALUE. 


13 


mean  small  calorie  is  used,  that  is,  one  one-hundredth  of  the  heat 
required  to  heat  1  gram  of  water  from  0°  to  100°  C.,  equivalent  to 
4.1834  Joules.0  The  electrical  energy  developed  in  the  bomb  and 
measured  as  heat  would  then  be  expressed  in  calories  by  the  following 
formula : 

n«i™      _  volts  x  amperes  X  seconds 
4.1834" 

During  the  12  minutes,  or  720  seconds,  we  had  the  following  amount 
of  heat  evolved  in  the  bomb: 

1 1 .588  X  4.757  X  720  H- 4.1834  =  9,487.4  calories, 
and 

9,487.4  calories -T- 3. 7579°  rise  =  2, 524. 7  grams  water  equivalent. 

At  the  time  of  the  test  there  was  no  oxygen  in  the  bomb;  hence 
a  correction  for  the  amount  usually  present  in  the  bomb  must  be 
applied.  The  amount  of  oxygen  in  this  bomb  at  20  atmospheres 
pressure  equals  10.24  grams,  which,  multiplied  by  0.157 — the  specific 
heat  of  oxygen  at  constant  volume — equals  1.6  grams  water,  wliich 
must  be  added  to  the  results  found  for  the  whole  system,  giving 
2,524.7  +  1.6  =  2,526.3  grams  as  the  water  equivalent. 

For  the  8-minute  section  referred  to  we  have : 
11.580  X 4.76  X  480-^4.1834  =  6,324.5  calories, 
and 

6,324.5  -=-2.5004  =  2,529.3  grams.    Adding  1 .6  for  the  oxygen  to  it  gives 
a  water  equivalent  of  2,530.9. 

Two  other  tests  with  the  same  instruments  were  made,  one  having 
the  current  on  for  10  minutes  and  the  other  for  12  minutes,  and 
worked  out  in  the  manner  already  described,  the  results  of  the  three 
tests  being  given  in  Table  3  below. 

TABLE  3. — Water  equivalent  of  calorimeter  by  three  electric  tests. 


Test. 

Heat 
evolved  in 
the  bomh. 

Corrected 
rise  in  tem- 
perature. 

Water 
equivalent. 

Correction 
for  Os. 

Water 
equivalent 
corrected. 

Time. 
/Total  12  minutes  

Calories. 
9,  487.  4 

3.  7579 

Grams. 
2,524  7 

Grams. 
I  0 

Grams. 
2  52ti  3 

1 

(Last  8  minutes 

ti  324  5 

2  5004 

2  5'>9  3 

1  ti 

2  530  9 

(Total  10  minutes 

7  969  ti 

3  1374 

2  540  1 

1  ti 

2  541  7 

2 

\Last  6  minutes 

4,759  2 

1  8885 

2  520  1 

1  6 

''  5''1  7 

(Total  12  minutes..     . 

9,48<i.  9 

3  7003 

2  522  9 

1    ti 

2  524  5 

3 

\Last8minutes  

(1,313.0 

2.  4910 

2,534  3 

1  ti 

2  535.9 

The  average  water  value  of  the  three  tests  obtained  when  the  total 
heat  is  used  is  equivalent  to  2,530.8  grams  of  water,  and  when  the 
effect  of  the  last  8  and  6  minutes  of  the  electric  current  is  considered, 
the  average  water  value  is  equal  to  2,529.5  grams. 

a  A.  W.  Smith.     Monthly  Weather  Review  for  October,  1907,  p.  11. 


14 


METHODS  AND  STANDARDS  IN  BOMB  CALORIMETKY. 


These  results  are  about  4.6  per  cent  higher  than  that  calculated  from 
the  weights  and  specific  heats  of  the  material  of  the  bomb.  Among 
themselves,  the  results  agree  fairly  well,  an  indication  that  the  source 
of  error,  if  any  exists,  must  be  a  constant  one.  Suspicion  fell  upon 
the  ammeter,  which  already  had  an  initial  error  of  +0.16  ampere,  and 
the  possibility  of  electrolytic  action  upon  the"  water.  Another 
ammeter  was  used,  this  time  a  Weston'  instrument,  and  a  piece  of 
rubber  tubing  was  slipped  over  the  metal  connector  so  as  to  have  no 
metal  in  direct  contact  with  the  water.  Two  tests  were  made  under 
these  conditions,  the  electric  current  being  on  for  12  minutes  in  each 
case. 

Without  reproducing  the  readings  of  the  instruments,  etc.,  the 
total  heat  as  well  as  the  heat  evolved  in  the  bomb  during  the  last 
9  minutes,  the  corresponding  rise  in  temperature,  and  the  water 
equivalent  of  the  bomb  system  are  shown  in  Table  4. 

TABLE  4. —  Water  equivalent  of  calorimeter  by  two  electric  tests. 


Test. 

Heat 
evolved  in 
the  bomb. 

Corrected 
rise  in  tem- 
perature. 

Water 
equivalent. 

Correction 
for  O2. 

Water 
equivalent 
corrected. 

Time. 
/Total  12  minutes 

Calories. 
9  125.5 

°C. 
3.  6985 

Grams. 
2,467.3 

Grams. 
1.6 

Grams. 
2,  468.  9 

1 

\Last  9  minutes  '.  . 

6,  828.  7 

2.  7550 

2,478.6 

1.6 

2,480.2 

(Total  12  minutes  

9,066.1 

3.  6710 

2,469.6 

1.6 

2,471.2 

2 

\Last  9  minutes 

6,790  5 

2,  7445 

2  474.2 

1.6 

2,  475.  8 

With  instruments  of  this  kind  where  the  hundredth  part  of  an 
ampere  or  volt  has  to  be  estimated  it  can  not  be  claimed  nor  expected 
that  the  results  should  be  reliable  to  within  ±0.5  per  cent.  The 
average  of  the  above  water  equivalents  equals  2,474  grams,  which 
is  still  over  2  per  cent  above  that  computed  from  the  specific  heats. 
It  was  therefore  decided  to  test  one  more  possible  source  of  error, 
viz,  the  evaporation  of  water  from  the  system  under  the  existing 
laboratory  conditions. 


ERROR  DUE  TO  EVAPORATION  OP  WATER. 


The  evaporation  from  the  surface  of  the  water  in  the  cylinder  con- 
taining the  bomb  is  held  to  be  of  so  little  consequence  that  it  is  gen- 
erally entirely  neglected,  but  the  writer  made  a  few  tests  in  order  to 
get  results  which  should  apply  to  this  apparatus,  locality,  and  labo- 
ratory. In  the  Atwater-Hempel  bomb  calorimeter  the  water  cylin- 
der is  surrounded  by  two  separate  dead-air  spaces,  and  the  two  covers 
for  these  spaces  are  of  smooth  hard  rubber.  These  covers  fit  snugly, 
so  that  practically  there  can  be  no  currents  in  the  inclosed  air. 

The  tests  were  made  in  the  following  manner:  The  water  cylinder 
was  filled  with  water  to  the  same  level  as  when  the  bomb  is  in  place. 
The  stirrer  was  placed  in  the  water,  and  to  represent  the  two  rubber- 


ERROR   DUE   TO   EVAPORATTOX    OF    WATER. 


15 


covered  connecting  wires  for  the  electric  current,  two  similar  small 
pieces  of  rubber-covered  wire  were  suspended  from  the  edge  of  the 
vessel  dipping  into  the  water.  The  cylinder  was  then  weighed  to  0.01 
gram  and  the  exact  time  noted.  It  was  then  quickly  put  in  its  place 
and  the  stirrer  operated  as  during  a  combustion  for  from  15  to  30 
minutes.  The  time  of  starting  and  stopping  the  stirrer,  as  well  as 
the  time  of  weighing,  was  noted. 

These  evaporation  tests  were  carried  on  in  the  calorimeter  both 
with  the  stirrer  in  operation  and  with  the  stirrer  standing  undisturbed, 
but  covered.  The  water  was  also  left  standing  exposed  to  the  air  of 
the  laboratory  in  a  place  where  there  was  no  draft.  Standing  exposed 
in  the  laboratory,  the  average  of  several  trials  was  0.0193  gram  of 
water  evaporated  per  minute,  whereas  standing  covered  in  the  bomb 
calorimeter  the  evaporation  was  only  0.0034  gram  per  minute. 
When  the  stirrer  was  in  operation,  the  evaporation  increased.  Below 
are  given  the  details  of  one  of  the  trials: 

TABLE  5. — Evaporation  of  water  from  calorimeter. 


Items. 

Time. 

Weight  of  ves- 
sel +  water, 
stirrer,  etc. 

Stirrer  started   ..        

9.40  a.  m  

Grams. 

10.  10  a.  m 

Difference  . 

30  minutes. 

Weight  before  taken                                                                                 * 

9.  3X  a.  m 

3  COO  5(> 

Weight  after  taken  . 

10.  13  a.  m. 

3.600.  12 

Difference 

35  minules 

44 

Temperature  of  room,  21°  C. 
Temperature  of  water,  21°  C. 
Time  of  stirring  the  water,  30  minutes. 
Time  required  for  handling,  5  minutes. 
Correction  for  5  minutes,  5X0.0193=0.097  gram  H,0. 

0.44—0.097=0.343  gram  evaporated  during  30  minutes,   or  0.0114  gram  per 
minute. 

Ten  trials  showed  the  following  rates  of  evaporation  per  minute: 

Gram. 
No.  1 . .  .  0.  00<J7 


No.  2... 
No.  3... 
No.  4... 
No.  5... 
No.  6... 
No.  7... 
No.  8... 
No.  9... 


0113 

0075 

0122 

0114 

0085 

0107 

0044 

0048 

No.  10...  .0075 


Average 0085 


16  METHODS  AND   STANDARDS   IN   BOMB   CALORIMETRY. 

These  tests  were  made  between  November  30  and  January  17. 

The  above  evaporation,  though  small,  makes  a  correction  which 
should  not  be  neglected,  especially  when  small  charges  are  used,  or 
charges  in  any  way  differing  from  the  quantity  used  in  the  stand- 
ardization of  the  apparatus.  The  heat  of  water  at  21°  C.  is,  accord- 
ing to  Prof.  A.  W.  Smith,0  equal  to  585.26  mean  calories  for  1  gram 
of  water. 

If  we  apply  the  above  correction  to  the  last-mentioned  electric 
tests  (Table  4)  it  would  be  166  minutes  X  0.008  gram  H2O  =  0.128 
gram  H2O  and  0.128x585.26  =  74.93  calories  to  be  subtracted  from 
the  calories  given  in  the  first  column  opposite  the  total  for  12  minutes. 
For  the  9  minutes  section  the  correction  would  be  9  X  0.008  =  0.072 
gram  H2O,  and  0.072x585.26  =  42.14  calories.  Recalculating,  the 
four  water  values  would  be: 

2,  447.  09 
2, 463.  36 
2,  449.  24 
2,  458.  87 

Average=2, 454.  64 

This  corrected  average  water  value  is  still  over  1.3  per  cent  greater 
than  that  computed  according  to  the  first  method,  and  the  difference 
is  undoubtedly  too  large  to  be  ascribed  to  the  manipulation  or  reading 
of  the  instrument.  In  all  probability  some  electrolysis  of  water 
must  have  taken  place  in  spite  of  the  precaution  taken,  and  we  can 
not  be  sure  on  this  point,  since  the  connection  was  not  dry.  Any 
error  due  to  condensation  of  moisture  on  the  outside  of  the  water 
vessel,  and  subsequent  evaporation  of  the  same,  has  not  been  ob- 
served and  can  at  best  be  but  small. 

The  evaporation  tests  may  throw  some  light  upon  this  problem  of 
condensation,  etc.  The  inner  air  space  or  layer  of  air  which  sur- 
rounds the  water  cylinder  in  the  calorimeter  equals  about  4  liters. 
At  22°  C.  these  4  liters  of  air  when  saturated  would  contain  0.0772 
gram  of  water.  In  about  9  minutes,  therefore,  perfectly  dry  air 
should  become  fully  saturated  and  the  evaporation  cease.  This  is 
not  the  case.  The  tests  showed  that  the  evaporation  continued 
unchecked,  and  in  the  particular  test  already  referred  to  there  was  a 
loss  of  0.343  gram  of  water  in  30  minutes,  enough  water  to  saturate 
17.8  liters  of  dry  air.  But  since  the  air  in  the  calorimeter  laboratory 
always  contains  some  moisture,  in  reality  a  much  larger  volume  of 
air  would  be  saturated.  The  fiber  envelope  is  supposed  to  be  water- 
proof, and  hence  it  is  very  unlikely  that  the  water  vapor  is  absorbed. 
It  would  seem  that  the  water  vapor  which  is  produced  at  the  surface 
of  the  water,  near  the  cover,  escapes  to  the  outside  by  means  of  its 

«  Physical  Review,  Vol.  XXV,  No.  3,  Sept.,  1907,  p.  170. 

&This  refers  to  the  total  time  influenced  by  the  evaporation  of  water  when  the  total 
heat  generated  during  the  full  time  of  12  minutes  is  considered. 


EKKOR  DUE   TO  EVAPORATION   OF   WATER.  17 

own  pressure  through  the  openings  in  and  around  the  cover.  This 
unchecked  evaporation  and  free  escape  of  the  vapor  seems  to  indicate 
that  the  inclosed  air  need  not  necessarily  be  affected  much,  except  at 
the  very  top,  and  that  the  air  layer  around  the  water  cylinder  is 
slowly  changed  by  diffusion  and  convection  currents. 

A  direct  test,  by  a  wet  and  a  dry  bulb  thermometer,  which  were 
6.0°  C.  apart  when  standing  quietly  in  the  laboratory,  showed  that 
there  was  no  effect  whatever  upon  the  moisture  conditions  in  the  air 
space  during  10  minutes'  operation  of  the  bomb.  These  thermom- 
eters, bulbs  one-third  down  in  the  space,  stood  3.0°  C.  apart  and 
remained  so;  hence  there  could  be  no  condensation  of  moisture  on 
the  sides  of  the  vessel. 

If,  now,  the  water  cylinder  as  it  is  placed  in  position  is  a  little  (say 
0.5  to  1°  C.)  colder  than  the  air  surrounding  it,  and  the  air  is  saturated 
with  moisture,  condensation  would  begin,  but  the  conditions  in  the 
bomb  room  have  never  at  the  time  of  making  a  combustion  been 
such  that  a  condensation  would  have  taken  place  at  the  start  with 
only  one  degree  difference  in  temperature.  The  water  cylinder  is  in 
the  calorimeter  only  a  few  minutes,  as  a  rule,  before  the  substance  is 
ignited,  and  it  is  questionable  if  in  that  length  of  time  the  conditions 
of  the  air  have  changed  enough  so  that  a  condensation  can  take  place, 
except,  perhaps,  at  the  upper  rim  of  the  vessel.  In  less  than  a  minute 
after  ignition,  the  temperature  of  the  wTater  is  higher  than  that  of  the 
surrounding  air,  and  hence  evaporation  of  any  water  which  had  been 
condensed  on  the  vessel  before  the  ignition  took  place  would  begin. 
Whether  any  condensation  or  evaporation  does  take  place  has  not 
been  experimentally  demonstrated,  but  from  the  very  nature  of  the 
existing  conditions  at  this  place,  errors  due  to  them  may  be  assumed 
to  be  entirely  negligible. 

As  a  check  on  these  evaporation  results,  on  a  clear  bright  day  a 
special  test  was  made  as  follows:  The  water  cylinder,  filled  with 
water  to  within  one-half  inch  of  the  top,  was  placed  in  position  in  the 
calorimeter  container,  as  during  an  energy  determination,  but  with- 
out the  stirrer.  The  covers  were  put  on  as  before  and  the  cylinder 
was  allowed  to  stand  for  20  minutes.  It  was  taken  out  and  reweighed 
quickly,  and  put  back  the  second  time  for  20  minutes.  After  that  it 
was  allowed  to  stand  in  the  laboratory  for  24  minutes  before  being 
weighed,  another  weight  being  taken  S*ininutes  later.  During  this 
laboratory  test  the  windows  and  doors  were  closed  so  that  there  was 
no  draft  to  influence  the  evaporation.  Next,  a  piece  of  paraffined 
paper  was  fitted  over  the  top  of  the  water  cylinder  and  sealed  by 
means  of  melted  soft  wax.  The  cylinder  was  weighed  and  put  in 
position  in  the  calorimeter  container  as  before  and  reweighed  after  20 
minutes.  After  that  it  was  allowed  to  stand  in  the  laboratory  and 


18 


METHODS  AND   STANDARDS   IN   BOMB   CALORIMETEY. 


was  weighed  after  different  intervals.     The  results  are  as  given  in 
Table  6. 

TABLE  G. — Evaporation  tests. 


Method. 

Water  cylinder. 

Evaporation  per 
minute. 

Time 
weighed. 

Weight. 

Time 
placed  in 
position 
and 
removed. 

In  labora- 
tory. 

In  bomb 
room. 

CYLINDER  UNCOVERED. 

9.14  a.  m 

Grams. 
3,  480.  43 

9.15  a.  m 

Gram  H»O. 

Gram  HZO. 
0.0035 

Difference  

9.3CU  a.  m... 

3,480.32 

9.35  a.  m.  . 

22J  mins  

.11 

20  mins.  .. 

9.36A  a.  m 

3,  480.  32 
3.480.21 

9.37  i  a.  m. 
9.57J  a.  m. 

Difference  

9.58  a.  m  

21J  mins  .11 

20  mins.  .. 

Average  . 

Laboratory,  first  trial 

9.58  a.  m.. 

3.4X0.21 

0.  0197 
0.0000 

Difference 

10.22  a.  m            3,479.71 

24  mins  .  .  . 

.50 

Laboratory,  second  trial 

10.22  a.  m 

3,479.71 

10.30  a.  m... 

3,  479.  58 

8  mins 

,13 

A  verage 

CYLINDER  SEALED. 

Bomb  room                                                     10.37  n.  m 

3,483.80 

10.59  a.  m 

3.  483.  80 

22  mins 

0.00 

10.59  a.  m 

3,  483.  80 

0.0000 

Difference.  . 

11.29  a.  m 

3,  483.  86 

30  mins  

0.00 

Laboratory,  second  trial 

11.29  a.  m 

3,  483.  8G 
3,483.87 

Difference 

2.46  p.  m 

197  mins.  .  .. 

+  .01 

Average 

From  this  test  we  see  that  the  change  in  weight  of  the  water  cylin- 
der in  the  previous  tests  was  due  entirely  to  evaporation  from  the 
surface  of  the  liquid  water,  and  that  there  was  no  condensation  on  the 
sides  of  the  cylinder  or  evaporation  of  any  condensed  moisture. 
During  the  test  the  temperature  of  the  bomb  room  was  24°  C.,  and 
the  wet-bulb  thermometer  (having  the  bulb  surrounded  by  a  piece  of 
moistened  filter  paper  and  swung  back  and  forth)  registered  16°  C. 
The  temperature  of  the  water  was  24°  C.,  and  in  the  laboratory  the 
dry  thermometer  registered  26.5°  C.,  and  the  wet-bulb  thermometer 
16°  C. 

The  water  equivalent  of  the  bomb  as  determined  by  the  electrical 
tests  which  have  been  described  is  not  satisfactory,  but  the  tests 


NEW   METHOD  FOE   DETERMINING   WATER  VALUE.  19 

have,  nevertheless,  been  useful  and  seem  to  justify  the  following 
conclusions : 

1.  The  tendency  of  the  electric  method  is  to  give  results  that  are 
too  high. 

2.  There  are  many  chances  for  error  connected  with  an  electric 
test,  even  if  the  instruments  used  have  been  carefully  calibrated. 

3.  Instruments  which  can  be  read  to  the  hundredth  part  of  an 
ampere  and  volt  only  by  estimation  are  not  accurate  enough  for  the 
best  work. 

4.  There  is  a  possibility  of  electrolysis  of  water;  hence  the  con- 
nection to  the  one  wire  in  the  bomb  should  not  only  be  insulated  from 
the  metal  of  the  bomb,  but  thoroughly  insulated  from  the  water 
surrounding  the  bomb  as  well. 

5.  The  tests  led  to  a  more  thorough  investigation  of  the  error  due 
to  evaporation  of  water  during  a  bomb  combustion,  showing  that 
under  usual  laboratory  conditions  there  is  an  error  which  must  be 
taken  into  account,  at  least  when  less  or  more  heat  is  generated  in 
the  bomb  than  was  generated  at  the  time  of  its  standardization. 

A    THIRD    METHOD. 

The  uncertainty  of  the  foregoing  results  prompted  the  working  out 
of  a  simple  and  perfectly  reliable  method  for  the  determination  of  the 
water  equivalent  of  the  calorimeter. 

The  principle  of  this  method  consists  in  burning  equal  charges  of  a 
substance  in  the  bomb,  first,  under  exactly  the  same  conditions  as 
when  a  heat  determination  is  made,  and,  secondly,  after  having,  with- 
out changing  any  of  the  external  conditions,  such  as  level  of  water, 
etc.,  reduced  the  water  equivalent  of  the  system.  The  same  amount 
of  oxygen  is  used  in  each  case.  From  the  difference  in  rise  of 
temperature  and  the  difference  in  water  equivalent  it  is  possible  to 
determine  very  accurately  the  water  value  of  the  calorimeter. 

By  this  method  it  is  possible,  first,  to  use  a  substance  of  unknown 
or  only  approximately  known  heat  of  combustion  and  an  oxygen 
supply  of  unknown  purity  to  determine  the  water  equivalent  of  the 
apparatus,  and  then  by  means  of  this  new  water  equivalent  and  the 
same  determinations  to  work  out  accurately  the  heat  of  combustion 
of  the  substance  used,  and  also  to  determine  the  correction  for  impu- 
rities in  the  oxygen,  if  any  such  were  present. 


DISPLACEMENT    OK    WATEH. 


When  the  bomb  and  stirrer  are  in  position  in  the  water  cylinder, 
there  is  a  space  above  the  bomb  and  one  near  the  bottom  where  part 
of  the  water  can  be  displaced,  and  thereby  the  water  equivalent  of  the 
system  reduced.  The  displacement  of  water  was  effected  by  two 


20  METHODS  AND   STANDARDS   IN   BOMB   CALOEIMETEY. 

double-walled  metal  rings.  The  one  to  fit  above  the  bomb  was  made 
of  sheet  lead  heavy  enough  to  rest  securely  by  its  own  weight.  The 
one  for  near  the  bottom  of  the  bomb  was  made  of  sheet  zinc  and  was 
held  in  position  by  the  bomb  itself,  hence  it  could  be  lighter  than  the 
water  displaced.  These  rings  were  so  made  that  they  did  not  touch 
the  sides  of  the  water  cylinder  or  in  any  way  interfere  with  the  oper- 
ation of  the  stirrer  or  the  thorough  mixing  of  the  water.  The  upper 
and  heavier  ring  contained  553.5  grams  of  lead  and  solder  and  25.8 
grams  of  zinc,  and  had  a  displacement  of  306  grams  of  water.  The 
lower  ring  contained  86  grams  of  zinc  and  20.9  grams  of  solder  and 
had  a  displacement  of  162  grams  of  water. 

The  computed  water  equivalent  of  the  metal  rings  was: 

Lead  (+solder)  574.4  gramsXO.0315  sp.  heat  « =18.09 

Zinc  111.8  gramsXO.0956  sp.  heat  a =10.68 

Total 28.  77 

During  a  heat  of  combustion  determination  the  bomb  is  immersed 
in  2,000  grams  of  water,  which  covers  the  highest  point  of  the  bomb 
to  a  certain  depth.  When  the  metal  rings  were  used,  a  quantity  of 
1,532  grams  of  water  brought  the  water  level  to  this  same  height. 
To  these  1,532  grams  of  water  must  be  added  the  28.8  grams  water 
equivalent  of  the  metal.  Thus  we  have  a  difference  of  2,000  grams 
-  1 ,560.8  =  439.2  grams  of  H2O,  or  439.2  X  0.99745  =  438. 1 ,  in  the  water 
equivalent  of  the  calorimeter  at  22.12°  C.,  the  temperature  at  which 
the  determinations  of  water  value  were  made,  without  changing  any 
of  the  other  conditions.  If,  now,  exactly  equal  weights  of  a  sub- 
stance and  fuse  wire  are  burned,  that  is,  if  the  same  amount  of  heat 
is  generated  in  the  bomb  while  it  is  immersed  in  the  two  different 
quantities  of  water,  there  will  be  a  difference  in  the  rise  of  temperature, 
and  we  have  the  necessary  factors  for  the  computation  of  the  water 
value. 

It  is,  however,  a  tedious  and  difficult  manipulation  to  press  and 
weigh  out  to  the  accuracy  of  0.0001  gram  a  charge  of  dry,  and  per- 
haps hygroscopic  material,  and  it  is  much  more  convenient  and  just 
as  accurate  to  weigh  out  approximately  equal  quantities  of  the  sub- 
stance for  each  charge,  and  then,  by  one  or  the  other  of  the  two 
methods  of  calculation  to  be  described,  to  compute  the  water  equiva- 
lent of  the  apparatus. 

In  the  following  table  (Table  7)  are  shown  the  results  of  a  number 
of  combustions  of  about  equal  charges  of  benzoic  acid  made  under 
the  two  conditions,  representing  a  difference  of  439.2  grams  of  water, 
equal  to  438.1  grams  water  equivalent  of  the  system  at  22°  C. 

o  Beilage  zum  Chemiker  Kalender,  1904. 


DETERMINATION   OF   WATER   VALUE. 


21 


TABLE  7. — Rise  in  temperature  due  to  burning  like  quantities  ofbenzoic  acid  in  the  bomb, 
with  20  atmospheres  oxygen  pressure,  but  with  varying  amounts  of  water  in  the  apparatus, 
there  being  a  difference  of  439-2  grams  of  ivater  equal  to  438.1  water  equivalent. 


Rise  in 

Water  used. 

Benzole 
acid 
burned. 

Fuse  wire. 

IINOj 
formed. 

tempera- 
ture (not 
corrected 
for  evapo- 
ration or 
impurities 

Rise  in 
tempera- 
ture due  to 
wire  and 
HN03. 

Rise  due 
to  l>enzoic 
acid. 

Rise  due 
tol 
pram  of 
tienzoic 
acid. 

in  oxygen). 

Gram*. 

Gram. 

Calories. 

Calories. 

0  C. 

"  C. 

0  C. 

0  C. 

2,000  

0  7157 

26.24 

7.10 

1.8837 

0.  01378 

1.86992 

2.  61272 

2000 

7341 

22.88 

7.20 

.9293 

.  01244 

1.91686 

2.61117 

2,000    . 

7034 

26.24 

6.90 

.8476 

.  01370 

1.83390 

2.  60719 

2,000    

7162 

23.04 

6.95 

.8826 

.  01240 

1.87020 

2.61128 

2,000  

7110 

26.56 

6.95 

.8726 

.01386 

1.85874 

2.  61426 

2,000  

7045 

23.68 

6.95 

.8510 

.01266 

1.83834 

2.60943 

Average  . 

2.61101 

1,560.8  

7122 

26.24 

8.25 

2.  2937 

.01741 

2.  27629 

3.1%1  4 

1,560.8  

6990 

26.24 

7-15 

2.  2467 

.01686 

2.  22984 

3.19004 

1,560.8  

7031 

26.24 

7.40 

2.  2606 

.01698 

2.  24362 

3.  19104 

1,560.8  

7028 

26.24 

7.&5 

2.2524 

.  01721 

2.  23519 

3.18041 

Average 

3.  18941 

Difference  in  rise  of  temperature,  0.57840°  C. 


WATER    VALUE    OF    THE    CALORIMETER. 


Two  methods  can  be  employed  to  compute  the  water  equivalent  of 
the  apparatus  from  the  above  determinations. 

One  method  is  to  make  use  of  the  approximate  heat  of  combustion 
value  of  benzoic  acid,  compute  the  total  heat  generated  by  each 
charge,  the  fuse  wire,  and  the  nitric  acid,  and  from  the  average  differ- 
ence in  rise  of  temperature  due  to  a  given  difference  in  the  water 
equivalent  of  the  calorimeter  to  compute  the  water  equivalent  of  the 
apparatus.  The  approximate  heat  of  combustion  value  of  the  sub- 
stance burned  is  computed  from  the  combustions  made  under  normal 
conditions,  using  the  computed  water  value  for  the  calorimeter,  i.  e., 
2,418.74  grams.  The  approximate  heat  of  combustion  of  benzoic 
acid  computed  in  this  way  would  be  6,315.3  calories  per  gram. 

The  second  method  consists  in  finding  the  value  of  the  number  of 
calories  represented  by  the  fuse  wire  and  the  nitric  acid  of  each  charge 
in  terms  of  degrees  rise  in  temperature,  subtracting  this  from  the 
observed- rise  in  temperature,  and  then  expressing  the  rise  in  tem- 
perature as  per  gram  substance  burned.  The  water  equivalent  of 
the  apparatus  is  calculated  from  the  average  difference  in  the  rise 
of  temperature  per  gram  and  the  difference  between  the  two  water 
equivalents.  This  method  of  computing  is  perhaps  preferable  to  the 
former,  and  since  the  corrections  for  the  wire  and  the  nitric  acid  are 
small  at  best,  it  may  be  more  correct  in  case  there  should  be  much  vari- 
ation in  the  size  of  the  charges  used  for  combustion.  In  Table  7  the 
rise  per  1  gram  of  the  substance  has  been  obtained  according  to  this 


22  METHODS  AND   STANDARDS   IN    BOMB   CALOKIMETRY. 

method.  To  find  the  rise  of  temperature  of  the  calorimeter  due  to 
the  burning  of  the  wire  and  formation  of  HNO3,  we  use  the  calcu- 
lated water  equivalent  of  the  apparatus,  viz,  2,418.74  grams  and 
1,980.64  grams,  respectively.  Taking  as  an  example  the  first  deter- 
mination in  Table  7,  we  have: 

2,418.74  :  (26.24  +  7.10)  :  :  1  :X 
X  =  0.01378°C. 

From  Table  7  we  learn  that  1  gram  of  the  substance  (in  this  case 
benzoic  acid)  burned  under  the  normal  conditions  caused  a  rise  in  tem- 
perature equal  to  2.61101°  C.  and  burned  when  the  water  equiva- 
lent was  reduced  by  438.1  grams,  caused  a  rise  in  temperature  of 
3.18941°  C.,  the  difference  being  0.57840°  C. 

Letting  X  =  water  equivalent  of  the  bomb  calorimeter,  we  have 

2.61101  X  =  3. 18941  (X- 438.1  grams) 
X  =  2,415. 77  grams. 

Computed  according  to  the  first  method,  the  water  value  of  the 
bomb  calorimeter  would  be  2,415.74  grams,  which  is  practically 
identical  with  the  foregoing,  and  2,415.77  is  considered  as  being  the 
correct  water  equivalent  of  this  calorimeter  and  will  be  used  in  all 
computations.  It  is,  of  course,  the  water  value  at  22.12°  C.,  corre- 
sponding to  a  specific  heat  of  water  of  0.99745  (compare  p.  20), 
expressed  in  terms  of  mean  calories,  i.  e.,  of  water  at  specific  heat  1.0. 
It  will  be  seen  that  this  agrees  very  closely  with  the  value  computed 
from  the  weights  and  specific  heats  of  the  materials  of  the  calorimeter; 
hence  the  latter  value  used  in  computing  the  rise  of  temperature  due 
to  the  combustion  of  the  fuse  wire  and  of  nitrogen  can  have  intro- 
duced no  appreciable  error. 

CORRECTION   FOR   COMBUSTIBLE   GASES    IN  TB33    OXYGEN. 

Having  the  water  value  of  the  apparatus  established,  the  next  step 
is  to  test  the  oxygen  supply  for  impurities  in  the  form  of  combustible 
gases,  etc.  This  is  very  important,  for  there  is  in  this  country  at 
the  present  time,  at  least  so  far  as  the  writer  knows,  no  perfectly 
pure  oxygen  put  up  under  high  pressure  for  bomb-calorimeter  use, 
and  hence  a  correction  must  be  worked  out  for  the  oxygen  used, 
when  accurate  work  is  required.  The  problem  may  be  established 
by  two  different  methods: 

First,  by  noting  the  influence  of  varying  pressure  of  oxygen  upon 
the  combustibility  of  the  gases  when  the  same  amount  of  heat  is 
generated  in  the  bomb  during  the  several  combustions. 

Secondly,  by  noting  the  effect  of  varying  charges,  that  is,  the 
varying  amounts  of  heat  evolved,  upon  the  combustion  of  the  differ- 
ent gases,  the  oxygen  pressure  in  the  bomb  being  the  same. 


CORRECTION   FOR   COMBUSTIBLE   GASES   IN    THE  OXYGEN.          23 

Analyzed  by  the  copper  oxid  combustion  method,  the  writer's  asso- 
ciate, Mr.  Braman,  found  the  oxygen  at  hand  to  contain  0.0161  per 
cent  of  carbon  and  0.0194  per  cent  of  hydrogen  by  weight,  and  the 
question  is:  Does  a  part,  or  all,  of  these  gaseous  impurities  burn  dur- 
ing an  energy  determination,  and,  if  burned,  what  will  be  the  rise  in 
temperature  caused  by  the  burning  ? 

This  bomb  charged  with  20  atmospheres  of  oxygen  would,  according 
to  the  above  analyses,  contain  0.001648  gram  of  carbon  and  0.001986 
gram  of  hydrogen.  The  ratio  of  carbon  to  hydrogen  is  such  that  they 
can  not  form  any  one  gas,  for  even  should  all  the  carbon  be  present 
as  methan,  there  would  still  be  0.00144  gram  of  free  hydrogen,  which 
alone  represents  about  50  calories. 

It  was  decided  to  burn  as  large  a  charge  of  benzoic  acid  as  would 
possibly  burn  completely  in  10  atmospheres  of  oxygen,  and  then  burn 
the  same  amount  in  20  atmospheres:  also  to  burn  about  half  the 
quantity  of  the  substance  in  oxygen  of  the  pressures  just  mentioned. 
The  final  results  of  these  tests  we  desire  to  express  in  terms  of  the 
quantity  of  heat  generated  in  the  bomb  and  its  effect  upon  the 
impurities  in  the  oxygen  instead  of  in  terms  of  any  particular  sub- 
stance. But  for  our  immediate  purpose,  we  can  express  the  rise  in 
temperature  in  terms  of  the  amount  of  charge  used,  and  hence  in  the 
computation  of  the  results  we  can  make  use  of  the  newly  found  water 
equivalent  and  follow  the  same  method  employed  in  finding  the  rise 
in  temperature  per  gram  of  substance  in  Table  7. 

Tables  8  and  9  contain  the  results  of  two  series  of  combustions  of 
like  charges  of  benzoic  acid  burned  in  different  amounts  of  oxygen 
and  the  rise  in  temperature  due  to  the  impurities  in  the  oxygen.  In 
the  first  series  of  combustions  the  charges  were  twice  the  size  of  those 
in  the  second  series.  The  carbon  present  in  the  form  of  C()2  in  the 
bomb  after  a  combustion  was  determined  in  some  instances  in  the 
case  of  the  large  charges  of  benzoic  acid,  and  the  average  of  three 
determinations  where  20  atmospheres  of  oxygen  were  used  was  68.801 
per  cent  of  carbon,  the  theoretical  being  68.83  per  cent  of  carbon. 
The  three  determinations  with  the  smaller  amount  of  oxygen  gave  an 
average  of  68.713  per  cent  of  carbon,  a  difference  of  about  0.09  per 
cent.  This  is  an  indication  that  the  charges  were  a  little  too  largo, 
so  that  with  10  atmospheres  of  oxygen  the  combustions  can  not  bo 
relied  upon  as  being  complete.  Assuming  that  this  small  difference 
in  carbon  represents  the  actual  difference  between  complete  and 
incomplete  combustion  of  the  benzoic  acid,  which  can  not  be  far 
wrong,  we  have  a  correction  which  can  be  applied  to  the  rise  in 
temperature  obtained  with  10  atmospheres  of  oxygen. 


24 


METHODS  AND   STANDARDS   IN   BOMB   CALORIMETEY. 


TABLE  8. — Rise  in  temperature  caused  by  burning  like  quantities  of  benzoic  add  in  vary- 
ing amounts  of  oxygen.     Results  corrected  for  0.032  gram  water  evaporation. 


Oxygen 
pressure. 

Benzoic 
acid 
burned. 

Fuse  wire. 

HNO3 
formed. 

Rise  in 
tempera- 
ture." 

Rise  in 
tempera- 
ture due  to 
wire  and 
HNO3. 

Rise  in 
tempera- 
ture due  to 
benzoic 
acid. 

Rise  due  to 
0.7142  gram 
benzoic 
acid. 

Atmospheres. 
20  

Gram. 
0.  7157 

Calories. 
26.24 

Calories. 
7.10 

•ft 

1.  8915 

°C. 
0.  01380 

°C. 
1.  87770 

°C. 

1.  87377 

20 

.7341 

22.88 

7.20 

1.  9371 

.  01246 

1.92464 

1  87247 

20. 

.7034 

26.24 

6.90 

1.8554 

.  01372 

1.  84168 

1.86996 

20  

.7162 

23.04 

6.95 

1.8904 

.  01242 

1.  87798 

1.87274 

20 

.7110 

26.56 

6.95 

1.8804 

.01388 

1.86652 

1.  87492 

20  

.7045 

23.68 

6.95 

1.8588 

.01268 

1.  84612 

1.87154 

Average 

1.  87257 

10 

.7108 

27.04 

1.73 

1.  8708 

.01191 

1.85889 

1.  86778 

10  

.7134 

23.36 

1.73 

1.  8752 

.  01039 

1.  86481 

1.86690 

10  

.7112 

21.  12 

1.73 

1.  8615 

.00946 

1.  85204 

1.85985 

Average 

1.86484 

' 

o  Corrected  for  evaporation  and  for  difference  in  water  value  of  calorimeter  due  to  differences  in  amount 
of  oxygen  used. 

0. 7142  gram  benzoic  acid  in  20  atmospheres  62 1. 87257  °C.  rise. 

.  7142  gram  benzoic  acid  in  10  atmospheres  62 1. 86484  °C.  rise. 

.  09  per  cent  incomplete  combustion  in  10  atmospheres  O? 00168  °C.  rise. 

Difference  due  to  10  atmospheres  oxygen 00605  °C. 

TABLE  9. — Rise  in  temperature  caused  by  burning  like  quantities  of  benzoic  acid  in  vary- 
ing amounts  of  oxygen.     Results  corrected  for  0.032  gram  water  evaporation. 


Rise  in 

tempera- 

Oxygen 

pressure. 

Benzoic 
acid 
burned. 

Fuse  wire. 

HNO3 
formed. 

ture  cor- 
rected for 
evapora- 
tion and 
variation 
in  bomb 

Rise  in 
tempera- 
ture due  to 
wire  and 
HNO3. 

Rise  in 
tempera- 
ture due  to 
benzoic 
acid. 

Rise  due  to 
0.3566  gram 
benzoic 
acid. 

water 

value. 

A  tmospheres. 

Gram. 

Calories. 

Calories. 

°C. 

°C. 

°C. 

"C. 

20 

0.3648 

22.88 

3.40 

0.9696 

0.  01088 

0.  95872 

0.  93717 

20 

.3579 

21.44 

3.40 

.9508 

.  01028 

.94052 

0.  93710 

Average 

.  93714 

10  

.3595 

23.04 

1.03 

.  95245 

.01000 

.  94245 

.  93484 

10 

.6301 

22.88 

1.03 

.  95215 

.00990 

.94225 

.93309 

10 

3585 

25.76 

1.03 

.  95315 

.01109 

.94206 

.  93707 

10  

.3484 

26.24 

1.03 

.  92385 

.01129 

.91256 

.93404 

Average 

.  93476 

0. 3566  gram  benzoic  acid  in  20  atmospheres  O2 0. 93714  °C.  rise. 

.  3566  gram  benzoic  acid  in  10  atmospheres  Os 93476  °C.  rise. 

Difference  due  to  10  atmospheres  Os 00238  °C. 

Difference  due  to  15  atmospheres  Oj 00357  °C. 

The  smaller  charges  (Table  9)  were  completely  burned  in  10  atmos- 
pheres of  oxygen,  which  was  proved  by  the  carbon  dioxid  determina- 
tion after  the  combustion  giving  68.838  per  cent  of  carbon.  From  the 
above  tables  we  learn  that  there  was  a  greater  rise  in  temperature 
when  the  combustion  took  place  in  oxygen  at  high  pressure  than 
when  less  oxygen  was  present.  In  the  case  of  the  smaller  charges, 


COMPARISON    OF   RESULTS   WITH   BENZOIC   ACID. 


25 


that  is,  less  heat  evolution,  the  difference  in  rise  of  temperature  was 
less  for  each  atmosphere  difference  in  pressure  than  in  the  case  of 
the  greater  heat.  It  is  difficult  to  remove  the  last  traces  of  a  com- 
bustible gas  from  a  gas  mixture  by  combustion  or  electric  sparks,  and 
we  can  not  expect  that  all  combustible  gases  present  in  the  oxygen 
would  be  burned  in  the  bomb  by  a  single  combustion  of  any  kind 
of  substance.  Further,  it  is  to  be  expected  that  conditions  may  be 
reached  relative  to  dilution  of  gases,  rate  of  combustion  of  the  sub- 
stance, and  heat  evolution  when  the  dilute  gases  escape  combustion 
altogether.  In  the  case  of  the  0.7142  gram  of  benzoic  acid  burned  in 
10  atmospheres  oxygen  pressure,  the  combustion  of  the  substance  was, 
as  stated,  not  quite  complete,  that  is,  vapors  or  combustible  gases 
from  the  burning  material  itself  had  begun  to  be  left  unburned. 
Hence  the  point  when  the  combustible  gases  present  in  the  oxygen 
supply  will  practically  cease  to  be  affected  can  not  be  far  either  way 
from  10  atmospheres  oxygen  pressure,  with  the  larger  charge  of 
benzoic  acid. 

In  order  to  compare  the  effect  of  the  0.3566-gram  charges  upon  the 
combustible  gases  with  that  of  the  larger  ones,  the  resulting  rises 
in  temperature  are  computed  to  the  same  basis  and  are  given  in 
Table  10. 

TABLE  10. — Comparison  of  average  results  obtained  by  burning  unlike  quantities  of 
benzoic  acid  in  like  amounts  of  oxygen. 


Oxygen. 

Benzoic 
acid 
charges. 

Average  rise 
in  tempera- 
ture. 

Rise   com- 
puted   on 
basis  of  0.7142 
grain  charge. 

Atmos- 

Gram. 

°C. 

°C. 

pheres, 

20 

0.7142 

1.  87257 

1.  S7257 

20 

.3500 

.93714 

1.S7691 

Difference 

+  .00434 

10 

.7142 

1.86484 

1.86652 

10 

.3566 

.  93476 

1.  87214 

Difference. 

+  .00562 

Here  we  notice,  first,  that  the  smaller  charges  show  a  relatively 
larger  rise  in  temperature  both  at  10  and  at  20  atmospheres;  further- 
more, the  small  charges,  which  burned  completely  at  10  atmospheres 
oxygen  pressure,  show  a  greater  increase  over  the  large  charges  at 
10  atmospheres  than  over  the  same  when  burned  at  20  atmospheres 
oxygen  pressure.  This  is  an  indication  that  the  limit  for  combustion 
of  the  gases  in  the  oxygen  has  not  been  reached  at  10  atmospheres 
with  a  small  charge.  With  0.3566  gram  charge,  therefore,  we  can 
well  assume  that  at  5  atmospheres  oxygen  pressure  the  conditions 
for  burning  correspond  to  those  at  10  atmospheres  with  0.7142  gram 
charge,  i.  e.,  twice  the  amount,  and  that,  therefore,  at  5  atmospheres 
oxygen  the  effect  upon  the  combustible  gases  would  have  ceased. 


26  METHODS  AND   STANDARDS   IN   BOMB   CALORIMETRY. 

Hence,  the  difference  in  rise  of  temperature  due  to  combustible  gases 
present  in  the  oxygen  supply  when  0.7142  gram  benzoic  acid  is  burned 
in  the  bomb  at  20  atmospheres  can  be  represented  by  0.0060°  C.  as 
found  in  Table  8,  and  for  0.3566  gram  charge  at  20  atmospheres 
oxygen  0.0036°  C.  (Table  9) ;  for  other  amounts  of  benzoic  acid  burned 
the  error  due  to  combustible  gases  is  found  by  interpolation. 

NATURE  OF  COMBUSTIBLE  GASES. 

As  to  the  nature  of  the  gas  or  gases  which  cause  the  rise  in  tem- 
perature, we  know  from  the  CO2  determinations  that  none  of  the 
carbon  in  the  oxygen  was  oxidized,  and  there  remains,  therefore,  only 
the  free  hydrogen,  even  a  portion  of  which  is  sufficient  to  cause  the 
observed  rise. 

THE  HEAT  OF  COMBUSTION  OF  BENZOIC  ACID. 

We  now  have  the  correct  water  equivalent  of  the  calorimeter,  a 
correction  for  the  impurities  in  the  oxygen,  and  also  the  evaporation 
correction,  and  can  proceed  to  the  computation  of  the  heat  of  com- 
bustion of  benzoic  acid. 

In  all  the  determinations  the  Regnault-Pf aundler  formula,  referred 
to  earlier  in  connection  with  the  water  value  determination  by  means 
of  electricity,  has  been  used  for  working  out  the  radiation  correction; 
that  is,  the  correction  for  the  influence  of  the  surrounding  air  upon 
the  readings.  The  computation  of  one  of  the  determinations  is 
given  below  in  detail  as  an  example,  and  following  that  will  be  found 
tabulated  the  results  of  various  determinations  representing  a  wide 
range  of  conditions,  both  in  regard  to  quantity  of  substance  burned 
and  oxygen  used.  It  is  a  satisfactory  check  upon  the  accuracy  of 
the  bomb  work  when  very  different  amounts  of  material  are  burned 
and  concordant  results  are  obtained. 

Example  of  a  determination  of  heat  combustion. 

Substance,  benzoic  acid,  Kahlbaum's. 

Charge,  0.7157  gram. 

Iron  fuse  wire  completely  burned,  0.0164  gram=26.24  calories. 

Oxygen  pressure,  20  atmospheres. 

Room  temperature,  23°  C. 

Water  temperature  before  ignition,  21.26°  C. 

HNO3  formed  and  titrated =7. 10  calories. 

Ignition  of  charge,  instantaneous. 

Combustion  of  substance,  complete. 

Carbon  dioxid  found  after  combustion =68. 801  per  cent  carbon. 

Thermometer  readings,  preliminary 1.438;  1.440;  1.442;  1.444;  1.445. 

Thermometer  readings,  corrected 1.4468;  1.4538. 

Combustion  period  readings 1.445;  2.920;  3.292;  3.316;  3.317. 

Combustion  period  readings,  corrected ..  1.4538;  2.9343;  3.3058;  3.3297;  3.3307. 

Thermometer  readings,  end  period 3.317;  3.313;  3.311;  3.309;  3.308. 

Thermometer  readings,  end  period,  corrected  ..  3.3307;  3.3208. 


THE   HEAT  OF  COMBUSTION   OF  BENZOIC  ACID. 


27 


r=0.0018 
f= 1.4503° 
0=5 

v=  -0.0025°  C. 

t=     3.3258°  C. 

Thermometer  lag=  -0.0005°  C. 


IAt= +0.0073°  C. 

Last  reading  of  combustion  period 

First  reading  of  combustion  period 

Radiation  correction 

Correction  for  thermometer  lag 

Correction  for  impurities  in  oxygen 

Evaporation  of  water  during  4  minutes 

Corrected  rise  in  temperature 


Water  value  of  bomb   system  with  20  atmospheres  oxygen 
(2415.8)  X1.88550  C  ...................................... 

Correction  for  fuse  wire  ..................................... 

Correction  for  HNO3  ........................................ 


0  C. 

+3.  3307 
-1.4538 
+  .0073 

-  .0005 

-  .0060 
+  .0078 

1.  8855 
Calories. 

4,  554.  99 
-26.  24 
-  7.10 


4,  521.  65 
4521.65-5-0.7157=6317.80  calories  per  gram  benzoic  acid. 

In  like  manner  all  the  results  found  in  the  following  table  are  worked 
out: 

TABLE  11.  —  Heat  generated  when  different  quantities  of  benzoic  acid  are  burned  in  varying 
amounts  of  oxygen,  and  the  heat  of  combustion  per  gram  of  benzoic  acid. 


Oxygen 
pressure. 

Henzoic 
acid, 
burned. 

Fuse 
wire. 

HN03 
formed. 

Observed 
rise  in 
tempera- 
ture. 

Corrected 
rise  in 
tempera- 
ture. 

Total  heat 
generated 
in  the 
bomb. 

Heat  per 
gram  ben- 
zoic acid. 

Tempera- 
ture of 
water  be- 
fore igni- 
tion. 

Atmos- 

pheres. 

Gram. 

Calories. 

Calories. 

0  C. 

O     ft 

Calories. 

Calorics. 

0  C. 

25 

0.7088 

23.36 

8.25 

1.8635 

1.8655 

4,  506.  75 

6,313.68 

21.3 

20 

.7157 

26.  24 

7.10 

1.8769 

.8855 

4,  554.  99 

6,317.67 

21.3 

20 

.7341 

22.88 

7.20 

1.9288 

.9311 

4,665.  15 

6.313.96 

20.8 

20 

.  7084 

26.  24 

6.90 

1.8408 

.8494 

4,  467.  79 

6.  304.  73 

20.7 

20 

.7162 

23.04 

6.95 

1.8804 

.8844 

4,552.34 

6.314.37 

21.4 

20 

.7110 

26.  56 

6.95 

1.8653 

.8744 

4,528.18 

6,321.62 

20.9 

20 

.7045 

23.  68 

6.95 

1.8435 

.8528 

4.  476.  00 

6,309.97 

21.3 

15 

.7100 

26.24 

4.40 

1.8448 

1.  86735 

4.511.15 

6.  3  10.  ,58 

20.4 

20 

.3648 

22.88 

3.40 

.9591 

.9660 

2,  .333.  67 

6,  325.  07 

20.4 

20 

.3579 

21.44 

3.40 

.9411 

.9472 

2,288.25 

6,  324.  13 

20.  3 

10 

.3595 

23.04 

1.03 

.9431 

.95125 

2.  298.  03 

6,  325.  33 

19.8 

10 

.3001 

22.88 

1.08 

.9427 

.95095 

2.297.31 

6.313.24 

19.9 

10 

.3585 

25.  76 

1.03 

.9390 

.95195 

2,  299.  73 

6,  340.  13 

20.5 

10 

.3484 

26.  24 

1.03 

.          .9095 

.  92265 

2.  228.  95 

6.319.38 

20.7 

Average 

6,318.  12 

20.7 

In  the  above  table  representing  fourteen  determinations  made 
under  such  varied  conditions  the  results  agree  very  well;  for  if  we 
leave  out  the  two  extreme  results  the  greatest  difference  from  the  aver- 
age in  the  remaining  twelve  determinations  is  but  8.15  calories.  Com- 
puted by  the  usual  formula,  the  probable  error  of  the  mean  of  the 


28  METHODS  AND  STANDARDS  IN   BOMB   CALOKIMETRY. 

fourteen  determinations  is  ±1.51  calories  and  the  probable  error  of 
a  single  determination  ±5.69  calories. 

SULPHUR,  PHOSPHORUS,  AND  CHLORIN. 

The  writer  sometime  ago0  called  attention  to  the  fact  that  the 
acid  found  in  the  bomb  after  a  combustion  is  not  always  HNO3  alone, 
and  that  it  is  especially  the  S  in  organic  combination,  which  goes  over 
into  gaseous  SO3  and  eventually  into  H2SO4,  that  needs  to  be  con- 
sidered. Hence  the  sulphuric,  phosphoric,  and  hydrochloric  acids 
are  determined  when  found  in  sufficient  quantities,  and  the  total 
acidity  found  by  titration  is  correspondingly  corrected  in  computing 
the  heat  arising  from  the  oxidation  of  free  nitrogen.  Determinations 
of  sulphur  and  phosphorus  have  been  successfully  carried  on  in  feeds, 
feces,  and  urines  by  the  bomb  method  during  these  last  three  years 
in  this  laboratory.  In  the  two  samples  of  benzoic  acid  which  were 
used  in  the  above  determinations,  one,  Kahlbaum's  best,  gave  no 
test  for  Cl.  and  only  a  light  trace  of  SO3.  The  other  sample,  "  Merck," 
gave  but  a  small  trace  of  SO3  and  a  distinct  trace  of  CL,  but  in  no 
case  enough  to  be  determined  for  the  sake  of  correction. 

CORRECTION    FOR    THE    SPECIFIC    HEAT    OF    WATER. 

Since  the  specific  heat  of  water  differs  at  different  temperatures, 
the  water  equivalent  of  the  calorimeter  will  also  vary  with  the  tem- 
perature. In  the  above  case  the  water  equivalent  was  determined 
with  an  average  of  21.08°  C.  water  temperature  before  the  combus- 
tions and  an  average  of  23.15°  after  the  combustions.  The  mean 
specific  heat  between  these  temperatures  is  0.99745.  The  mean 
specific  heat  between  the  average  temperatures  before  and  after 
combustions  in  the  fourteen  determinations  of  Table  11  is  0.99752. 

The  true  average  heat  of  combustion,  therefore,  is 


6,318.12  X;           =  6,318.56  calories.6 
99745 

CHANGE  IN  THE  BOMB  CONTENTS. 

There  are  at  least  two  other  conditions  which  should  be  consid- 
ered, since  they  may  to  some  small  degree  influence  the  heat  of  com- 
bustion as  computed  from  the  determinations  already  described  and 
recorded  in  Table  1  1  . 

One  is  a  possible  change  in  the  water  value  of  the  calorimeter 
which  may  be  caused  by  the  combustion  of  the  substance  in  the 
bomb.  According  to  the  nature  of  the  substance,  the  contents  of 

a  U.  S.  Department  of  Agriculture,  Bureau  of  Animal  Industry  Bulletin  94,  p.  32. 

b  This  method  of  computation  assumes,  of  course,  that  the  specific  heats  of  the 
materials  of  the  calorimeter  itself  vary  with  the  temperature  at  the  same  rate  as  does 
that  of  water.  The  total  correction  is  so  small,  however,  that  any  error  thus  intro- 
duced must  be  insignificant. 


CHANGE   IN   THE   BOMB   CONTENTS.  29 

the  bomb  will  change  more  or  less,  so  as  to  make  the  water  equiva- 
lent after  the  combustion  different  from  what  it  was  before. 

When  the  same  kind  of  material  is  burned  as  that  which  was  used 
for  the  determination  of  the  water  value  of  the  bomb,  the  changes 
need  not  be  considered  except  when  a  different  quantity  is  burned. 
Should  an  entirely  different  compound  be  burned,  even  if  in  a  quan- 
tity like  that  used  for  water  value  determinations,  the  condition 
existing  in  the  bomb  before  and  after  combustion  should  be  com- 
puted whenever  it  is  possible  to  do  so,  in  order  to  determine  whether 
enough  change  took  place  in  the  water  equivalent  of  the  bomb  to 
call  for  a  correction.  In  the  computations  we  use  the  following  values : 

Volume  of  gas  in  bomb  at  20  atmospheres,  measured  at  20°  C., 
730  mm.  pressure,0  is  8  liters. 

Grams. 

Weight  per  liter  O2  at  20°,  730  mm 1.  2798 

Specific  heat  (X,  constant  volume 157 

Specific  heat,  CO.,,  constant  volume 149 

Specific  heat  benzoic  acid,  computed 30 

Specific  heat  Fe3O4 167 

Specific  heat  Fe2 1114 

Specific  heat  HNO3 445 

Specific  heat  H20 1.  0000 

The  average  of  10  charges  used  in  the  water  value  determinations 
equals  0.7102  gram  benzoic  acid,  and  considering  all  the  gas  as  oxygen 
we  have  in  the  bomb  before  the  combustion  the  following  water 
equivalent : 

Grams  HjO. 

Benzoic  acid,  0.7102  gram  X0.30 0.  2131 

Oxygen,  8X1.2798X0.157 1.  6074 

Iron  wire,  0.0164  X0.1114 0018 


Total 1.  8223 

After  the  combustion  there  are  in  the  bomb  the  following  substances: 

Grams. 

Carbon  dioxid,  0.7102X2.5246 1.  7930 

Water,  0.7102X0.4426 3143 

FeaO,,  0.0164X1.381 0227 

Oxygen,  10.2384-1.4309 8.  8075 

N2O5 0275 

This  is  equivalent  to  the  following  amounts  of  II,O: 

Grams  lljO. 

1.7930  grams  C02X0.149 0.  2(572 

.3143  gram  H,OX  1.000 3143 

.0227  gram  Fe3O4X0.167 0039 

.0321  gram  HXO3X0.445 -0.0046 0097 

8.8075  grams  O2X0.157 1.  3S28 

Total 1.  9779 

Thus  with  benzoic  acid  there  is  a  change  of  only  about  0.10  gram 
water  equivalent  caused  by  the  combustion. 

"Average  for  this  locality. 


30  METHODS  AND   STANDARDS   IN   BOMB   CALORIMETBY. 

If  instead  of  benzoic  acid,  0.7  gram  of  ethyl  alcohol  were  burned, 
we  should  find  a  difference  of  about  0.39  gram  water  equivalent 
caused  by  the  combustion  and  about  0.44  gram  water  equivalent 
different  from  that  obtained  by  benzoic  acid.  The  average  charge 
hi  the  fourteen  determinations  of  Table  11  equals  0.5609  gram,  and 
the  average  charge  used  in  standardizing  the  bomb  was  0.7102  gram, 
which  is  equivalent  to  a  difference  of  0.08  gram  in  the  water  value  of 
the  bomb,  or  a  correction  of  —0.20  calorie  per  gram  in  the  average 
result.  This  is  a  very  small  correction  and  usually  need  not  be 
considered  at  all. 

CHANGE    OF   PRESSURE    IN    THE    BOMB. 

The  second  condition  referred  to  above  is  the  change  in  pressure 
in  the  bomb  resulting  from  the  combustion.  By  the  heat  of  com- 
bustion of  a  substance  is  generally  understood  the  heat  at  constant 
pressure,  which  is  in  many  instances  slightly  different  from  that 
determined  by  the  bomb  calorimeter  at  constant  volume.  Since  it 
is  the  difference  between  the  conditions  before  and  after  the  combus- 
tion which  is  considered,  it  makes  no  difference  what  pressure  the 
gases  may  be  under  in  the  bomb  before  the  combustion.  If  the 
pressure  of  the  gases  before  and  after  the  combustion  remains  the 
same,  the  heat  of  combustion  at  constant  volume  and  constant  pres- 
sure is  the  same.  Leaving  out  of  account  the  small  changes  due  to 
the  oxidation  of  iron  and  the  formation  of  nitric  acid  in  the  bomb, 
this  is  theoretically  true  of  carbohydrates  where  CO2  and  O2  replace 
each  other  volume  for  volume.  With  other  substances  it  may  be 
different.  At  constant  pressure  compounds  containing  much  hydro- 
gen will  cause  a  decrease  in  volume  of  the  gases  and  hence  require  a 
plus  correction,  and  compounds  with  less  hydrogen  but  plenty  of  nitro- 
gen may  cause  an  increase  in  gas  volume,  and  consequently  there  will 
be  a  minus  correction  to  the  results  obtained  by  the  bomb. 

For  a  solid  or  liquid  substance  of  the  composition  CnHpOq  burned 
at  constant  volume  in  the  bomb  the  heat  at  constant  pressure  is 
expressed  by  the  following  formula  :  ° 


=  CtV+0.5424       g-+  0.002        r 

where 

t  =  temperature. 

p  and  q  =  number  of  atoms  in  the  molecule. 

According  to  this  formula,  benzoic  acid,  C7H6O2,  at  constant  pres- 
sure will  be  : 

(HP  =  Ct  V+  0.5424  X^—  +  0.002X^-^X22.8° 

which  expressed  in  calories  per  gram  equals: 

6,318.56  +  2.41  =6,320.97  per  gram  benzoic  acid. 


«  Beila^e  zum  Ohemiker-Kalemler,  1904,  p.  144. 


USE  OF  BOMB  CALORIMETER  UNDER  DIFFERENT  CONDITIONS.        31 

If  to  this  we  apply  the  correction  found  for  the  change  in  the  bomb 
content  bepause  of  unlike  charges,  —  0.20  calorie,  the  heat  of  combus- 
tion of  1  gram  benzoic  acid,  C7H6O2,  at  constant  pressure  will  be: 
6, 320. 77  ±1.51  mean  calories,  a  value  practically  identical  with  that 
found  by  Stohman,  viz,  6,322  calories. 

USE    OF  THE    BOMB    CALORIMETER   UNDER    DIFFERENT    CON- 
DITIONS. 

Judging  from  these  investigations,  there  are  many  conditions 
which  may  influence  the  work  with  the  bomb  and  cause  the  results 
to  become  inaccurate,  and  the  question  is,  What  is  the  best  and  most 
convenient  way  to  operate  the  bomb  so  as  to  get  reliable  results 
under  the  various  conditions?  Three  methods  in  regard  to  the 
determination  of  the  water  value  of  the  calorimeter  and  its  use  may 
be  employed  according  to  existing  laboratory  and  other  conditions: 

1.  The   apparent  water  value  may  be    directly  determined    by 
burning  a  given  weight  of  a  standard  substance,  note  being  taken 
of  all  the  conditions  existing  at  the  time  of  standardization  of  the 
bomb,  including  amount  of  substance  and  of  oxygen,  and  atmospheric 
conditions   influencing   evaporation.     If,  now,  the   substance  to  be 
analyzed  corresponds  in  quantity  to  the  calories  generated  at  the 
standardization,  and  if  the  other  conditions  are  the  same,  there  will 
be  no  corrections  to  apply  for  impurity  in  oxygen  or  for  evaporation 
of  water.     Whether  the  small  correction  for  constant  volume  and 
for  change  in  contents  of  the  bomb  need  to  be  applied  depends  upon 
the  degree  of  accuracy  to  which  the  operator  expects  to  work. 

2.  Should  it  be  required  to  burn  charges  giving  much  more  or  less 
heat  than  that  used  for  standardization,  with  the  oxygen  supply  and 
evaporation  condition  remaining  unchanged,   then  it  is  most  con- 
venient to  have  the  water  value  of  the  bomb  determined  with  the 
smaller  or  larger  charges  also,  and  thus  avoid  the  use  of  corrections. 

3.  When,  however,  the  heat  determinations  must  be  made  under 
varying  temperature  conditions,  with  different  amounts  of  substance 
and  various  oxygen  supplies,  then  all  the  corrections  due  to  variation 
from  the  conditions  at  which  the  bomb  was  standardized  must  be 
applied. 

The  different  water  values  for  the  bomb  calorimeter  used  in  this 
work  corresponding  to  the  above  three  methods  of  usage  would  be, 
including  2,000  grams  of  water; 

Method  1,  with  0.7142  gram  benzoie  acid  charge,  2.421  water 
value. 

Method  2,  with  0.3614  gram  benzoic  acid  charge.  2,425.4  water 
value. 

Method  3,  with  0.7102  gram  benzoic  acid  charge,  2,415.7  water 
value. 

In  the  third  or  last  value,  the  corrections  due  to  evaporation  of 
water  and  specific  heat  of  water  have  been  applied. 


32 


METHODS  AND   STANDARDS   IN    BOMB    CALORIMETRY. 


CORRECTIONS    FOR    IMPURITIES    IN    OXYGEN. 

Having  now  the  specific  heat  of  combustion  of  benzoic  acid,  we 
can  find  from  Tables  8  and  9  the  correction  for  impurities  in  the 
oxygen  expressed  in  degrees  rise  of  temperature,  or  its  equivalent 
in  calories,  for  any  given  amount  of  heat  generated  in  the  bomb 
during  a  combustion.  All  substances  do  not  affect  the  combustible 
gases  alike,  but  for  this  purpose  we  may  assume  benzoic  acid  to  be  a 
representative  substance,  and  each  kind  of  material  need  not  be 
tested  separately.  The  average  of  six  charges  of  benzoic  acid  was 
0.7142  gram,  which,  multiplied  by  6,320.8  equals  4,514.3  calories. 
This  amount  of  heat  caused  a  rise  in  temperature  of  1.87257°  C.  with 
20  atmospheres  oxygen,  and  with  10  atmospheres  oxygen  a  rise  of 
1.86652°  C.,  a  difference  of  0.00605°  C.,  which  is  equal  to  14.62 
calories.  In  like  manner,  the  average  charge,  0.3566  grams  benzoic 
acid,  Table  9,  equals  2,254  calories  and  causes  a  total  difference  of 
0.00357°  C.  rise,  equivalent  to  8.59  calories. 

By  interpolation  we  have,  according  to  the  various  amounts  of  heat 
generated  in  20  atmospheres  oxygen  pressure,  the  corrections  for  the 
oxygen  shown  in  Table  12.  They  are  applicable,  of  course,  only  to  the 
particular  sample  of  oxygen  used  in  these  determinations,  and  unless  a 
uniform  quality  of  the  oxygen  in  this  respect  can  be  assured,  it  would 
be  necessary  to  redetermine  their  factors  for  each  cylinder  of  oxygen. 

TABLE  12. — Corrections  for  combustible  gases  in  oxygen. 


Heat  gene- 
rated in 
bomb. 

Correction  in  terms  of— 

Rise  of  tem- 
perature. 

Calories. 

Calories. 
4,500 
4,000 
3,500 
3,000 
2,500 
2,250 
2,000 

°C. 
0.00603 
0.00550 
0.00495 
0.00440 
0.00385 
0.00357 
0.  00330 

14.55 
13.22 
11.89 
10.57 
9.24 
8.58 
7.91 

BENZOIC  ACID  AS  A  STANDARD. 

From  his  experience  with  various  substances,  and  because  of  the 
value  obtained  for  benzoic  acid  as  described  in  this  paper,  the  author 
in  conclusion  urges  all  persons  using  the  bomb  calorimeter  for  scien- 
tific work  where  results  are  to  be  published,  for  the  sake  of  uniformity 
and  comparability  of  results,  to  adopt  benzoic  acid  as  the  one  single 
standard  against  which  to  standardize  the  bomb,  and  to  accept  6,322 
calories  per  gram  as  its  heat  of  combustion.  This  is  the  value  accred- 
ited to  Stohhmann,  and  this  value  ought  to  remain  the  standard  until 
it  has  been  definitely  proved  to  be  erroneous  and  a  new  value  in  some 
way  officially  recognized  or  accepted. 

o 


001  087839 


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